12,495 research outputs found
Parareal with a physics-informed neural network as coarse propagator
Parallel-in-time algorithms provide an additional layer of concurrency for
the numerical integration of models based on time-dependent differential
equations. Methods like Parareal, which parallelize across multiple time steps,
rely on a computationally cheap and coarse integrator to propagate information
forward in time, while a parallelizable expensive fine propagator provides
accuracy. Typically, the coarse method is a numerical integrator using lower
resolution, reduced order or a simplified model. Our paper proposes to use a
physics-informed neural network (PINN) instead. We demonstrate for the
Black-Scholes equation, a partial differential equation from computational
finance, that Parareal with a PINN coarse propagator provides better speedup
than a numerical coarse propagator. Training and evaluating a neural network
are both tasks whose computing patterns are well suited for GPUs. By contrast,
mesh-based algorithms with their low computational intensity struggle to
perform well. We show that moving the coarse propagator PINN to a GPU while
running the numerical fine propagator on the CPU further improves Parareal's
single-node performance. This suggests that integrating machine learning
techniques into parallel-in-time integration methods and exploiting their
differences in computing patterns might offer a way to better utilize
heterogeneous architectures.Comment: 13 pages, 7 figure
Segregated Runge–Kutta time integration of convection-stabilized mixed finite element schemes for wall-unresolved LES of incompressible flows
In this work, we develop a high-performance numerical framework for the large eddy simulation (LES) of incompressible flows. The spatial discretization of the nonlinear system is carried out using mixed finite element (FE) schemes supplemented with symmetric projection stabilization of the convective term and a penalty term for the divergence constraint. These additional terms introduced at the discrete level have been proved to act as implicit LES models. In order to perform meaningful wall-unresolved simulations, we consider a weak imposition of the boundary conditions using a Nitsche’s-type scheme, where the tangential component penalty term is designed to act as a wall law. Next, segregated Runge–Kutta (SRK) schemes (recently proposed by the authors for laminar flow problems) are applied to the LES simulation of turbulent flows. By the introduction of a penalty term on the trace of the acceleration, these methods exhibit excellent stability properties for both implicit and explicit treatment of the convective terms. SRK schemes are excellent for large-scale simulations, since they reduce the computational cost of the linear system solves by splitting velocity and pressure computations at the time integration level, leading to two uncoupled systems. The pressure system is a Darcy-type problem that can easily be preconditioned using a traditional block-preconditioning scheme that only requires a Poisson solver. At the end, only coercive systems have to be solved, which can be effectively preconditioned by multilevel domain decomposition schemes, which are both optimal and scalable. The framework is applied to the Taylor–Green and turbulent channel flow benchmarks in order to prove the accuracy of the convection-stabilized mixed FEs as LES models and SRK time integrators. The scalability of the preconditioning techniques (in space only) has also been proven for one step of the SRK scheme for the Taylor–Green flow using uniform meshes. Moreover, a turbulent flow around a NACA profile is solved to show the applicability of the proposed algorithms for a realistic problem.Peer ReviewedPostprint (author's final draft
Robust physics-based robotic manipulation in real-time
This thesis presents planners and controllers for robust physics-based manipulation in real-time. By physics-based manipulation, I refer to manipulation tasks where a physics model is required to predict the consequences of robot actions, for example, when a robot pushes obstacles aside in a fridge to retrieve an object behind them.
There are two major problems with physics-based planning using traditional techniques. First, uncertainty, both in physics predictions and in state estimation, can result in the failure of many physics-based plans when executed in the real-world. Second, the computational expense of making physics-based predictions can make planning slow and can be a major bottleneck for real-time control. I address both of these problems in this thesis.
To address uncertainty, first, I present an online re-planning algorithm based on trajectory optimization. It reacts, in real-time, to changes in physics predictions to successfully complete a manipulation task. Second, some open-loop physics-based plans succeed in the real-world under uncertainty. How can one generate such robust open-loop plans with guarantees? I provide conditions for robustness in the real-world based on contraction theory. I also present a robust planner and a controller. It autonomously switches between robust open-loop execution, and closed-loop control to complete a manipulation task. Third, a robot can be optimistic in the face of uncertainty. It can adapt its actions to the accuracy requirements of a task. I present such a task-adaptive planner that embraces uncertainty, pushing fast for easy tasks, and slow for more difficult tasks.
To address the problem of computationally expensive physics-based predictions, I present learned and analytical coarse physics models for single and multi-object manipulation. They are cheap to compute but can be inaccurate. On the other hand, fine physics models provide the best predictions but are computationally expensive. I present algorithms that combine coarse and fine physics models through parallel-in-time integration. The result is orders of magnitude reduction in physics-based planning and control time
A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials
This article has been made available through the Brunel Open Access Publishing Fund.A new multiscale finite element formulation
is presented for nonlinear dynamic analysis of heterogeneous
structures. The proposed multiscale approach utilizes
the hysteretic finite element method to model the microstructure.
Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments
Parareal with a Learned Coarse Model for Robotic Manipulation
A key component of many robotics model-based planning and control algorithms is physics predictions, that is, forecasting a sequence of states given an initial state and a sequence of controls. This process is slow and a major computational bottleneck for robotics planning algorithms. Parallel-in-time integration methods can help to leverage parallel computing to accelerate physics predictions and thus planning. The Parareal algorithm iterates between a coarse serial integrator and a fine parallel integrator. A key challenge is to devise a coarse model that is computationally cheap but accurate enough for Parareal to converge quickly. Here, we investigate the use of a deep neural network physics model as a coarse model for Parareal in the context of robotic manipulation. In simulated experiments using the physics engine Mujoco as fine propagator we show that the learned coarse model leads to faster Parareal convergence than a coarse physics-based model. We further show that the learned coarse model allows to apply Parareal to scenarios with multiple objects, where the physics-based coarse model is not applicable. Finally, we conduct experiments on a real robot and show that Parareal predictions are close to real-world physics predictions for robotic pushing of multiple objects. Code (https://doi.org/10.5281/zenodo.3779085) and videos (https://youtu. be/wCh2o1rf-gA) are publicly available
Theory of pressure acoustics with boundary layers and streaming in curved elastic cavities
The acoustic fields and streaming in a confined fluid depend strongly on the
acoustic boundary layer forming near the wall. The width of this layer is
typically much smaller than the bulk length scale set by the geometry or the
acoustic wavelength, which makes direct numerical simulations challenging.
Based on this separation in length scales, we extend the classical theory of
pressure acoustics by deriving a boundary condition for the acoustic pressure
that takes boundary-layer effects fully into account. Using the same
length-scale separation for the steady second-order streaming, and combining it
with time-averaged short-range products of first-order fields, we replace the
usual limiting-velocity theory with an analytical slip-velocity condition on
the long-range streaming field at the wall. The derived boundary conditions are
valid for oscillating cavities of arbitrary shape and wall motion as long as
the wall curvature and displacement amplitude are both sufficiently small.
Finally, we validate our theory by comparison with direct numerical simulation
in two examples of two-dimensional water-filled cavities: The well-studied
rectangular cavity with prescribed wall actuation, and the more generic
elliptical cavity embedded in an externally actuated rectangular elastic glass
block.Comment: 18 pages, 5 figures, pdfLatex, RevTe
Multifarious Hierarchies of Mechanical Models for Artist Assigned Levels-of-Detail
International audienceWe present a new framework for artist driven level of detail in solid simulations. Simulated objects are simultaneously embedded in several, separately designed deformation models with their own independent degrees of freedom. The models are ordered to apply their deformations hierarchically, and we enforce the uniqueness of the dynamics solutions using a novel kinetic filtering operator designed to ensure that each child only adds detail motion to its parent without introducing redundancies. This new approach allows artists to easily add fine-scale details without introducing unnecessary degrees-of-freedom to the simulation or resorting to complex geometric operations like anisotropic volume meshing. We illustrate the utility of our approach with several detail enriched simulation examples
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